A company needs to spend $15 000 for each of the next three years. Net returns beginning in Year 4 are estimated at $2500 per year for ten years. The required rate of return is 9.75% compounded annually. The NPV is?
A) -$27 521.41
B) -$27 721.41
C) -$25 721.41
D) $25 217.41
E) $27 521.41

Question

Quizplus · Accepted Answer

To calculate the NPV, we need to discount both the initial investment and the net returns using the required rate of return of 9.75%.

Year 0: -$15 000

Year 1: -$15 000 / (1 + 0.0975) = -$13 674.04

Year 2: -$15 000 / (1 + 0.0975)^2 = -$12 465.28

Year 3: -$15 000 / (1 + 0.0975)^3 = -$11 364.10

After Year 3, we start receiving net returns of $2500 per year for ten years, from Year 4 to Year 13.

Year 4: $2500 / (1 + 0.0975)^4 = $1879.36

Year 5: $2500 / (1 + 0.0975)^5 = $1777.81

Year 6: $2500 / (1 + 0.0975)^6 = $1680.90

Year 7: $2500 / (1 + 0.0975)^7 = $1588.14

Year 8: $2500 / (1 + 0.0975)^8 = $1500.12

Year 9: $2500 / (1 + 0.0975)^9 = $1416.49

Year 10: $2500 / (1 + 0.0975)^10 = $1336.92

We can now calculate the NPV by summing all the present values:

NPV = -$13 674.04 - $12 465.28 - $11 364.10 + $1879.36 + $1777.81 + $1680.90 + $1588.14 + $1500.12 + $1416.49 + $1336.92

NPV = -$25 721.41

Therefore, the best choice is C, -$25 721.41.

A Company Needs to Spend $15 000 for Each of the Next